Providing instruction on spatial geometry, specifically how to calculate the surface areas of composite solids, challenges many elementary school teachers. Determining the surface areas of composite solids involves complex calculations and advanced spatial concepts. The goals of this study were to build on students' learning processes for…

Eighth grade students in Australia (N = 60) participated in an experiment on learning how to solve percentage change problems in a regular classroom in three conditions: unitary, pictorial, and equation approaches. The procedure involved a pre-test, an acquisition phase, and a post-test. The main goal was to test the relative merits of the three…

It is commonly suggested to mathematics teachers to present learners different methods in order to solve one problem. This so-called "learning with multiple solution methods" is also recommended from a psychological point of view. However, existing research leaves many questions unanswered, particularly concerning the effects of…

This paper presents a small group computing environment in which four students each control a different point in a geometric space, such that as a group they collectively manipulate the vertices of a quadrilateral. Prior research has revealed that students have considerable difficulty in learning about the interrelationships among quadrilaterals…

Students' judgments about "what counts" as mathematics in and out of school have important consequences for problem solving and transfer, yet our understanding of the source and nature of these judgments remains incomplete. Thirty-five sixth grade students participated in a study focused on what activities students judge as…

The mentor's background in educational roles has been presented as a moderator of School-Based Mentoring (SBM). However, the analysis of overlapping mentoring and teaching roles has been underemphasized in the literature. The aim of this study is to test whether the combination of mentoring and teaching roles influences the mentees'…

In the past technology products created to overcome accessibility and usability issues experienced by individuals with special needs have also resulted in greater usability for the wider population. Technology is increasingly being seen as a key component within the education of children with special needs and recently researchers have developed…

Educational research indicates that error reflection, especially reflection on incorrect examples, has a positive effect on knowledge acquisition. The benefit of error reflections might be explained by the extended knowledge of incorrect strategies and concepts (negative knowledge) which fosters the learning of new content. In a field experiment…

Twenty-four mathematics teachers were asked to think aloud when posing a word problem whose solution could be found by computing 4/5 divided by 2/3. The data consisted of verbal protocols along with the written notes made by the subjects. The qualitative analysis of the data was focused on identifying the structures of the problems produced and…

Many studies have tested external supports for promoting productive collaboration, but relatively few have examined what features characterize naturally productive collaborative tasks. Two lines of research have come to distinct conclusions on the primary task feature associated with productive collaboration: demonstrability versus complexity.…

Algebra students studied either static-table, static-graphics, or interactive-graphics instructional worked examples that alternated with Algebra Cognitive Tutor practice problems. A control group did not study worked examples but solved both the instructional and practice problems on the Cognitive Tutor (CT). Students in the control group…

In an attempt to address shortcomings revealed in international assessments and lamented in legislation, many schools are reducing or eliminating elective courses, applying the rationale that replacing "non-essential" subjects with core subjects, such as mathematics and language arts, will better position students in the global market. However,…

Does the specific structure of advance organizers influence learning outcomes? In the first experiment, 48 psychology students were randomly assigned to three differently structured advance organizers: a well-structured, a well-structured and key-concept emphasizing, and a less structured advance organizer. These were followed by a sorting task, a…

To promote student learning in a relearning situation in university-level mathematics, we developed the learning method TAU ("Think Ask Understand"). TAU provides support (i.e. a role script) for students' interaction during a collaborative problem-solving phase at the beginning of the learning process, while content-related instruction is delayed…

In a study with ninth-grade mathematics students on learning the concept of variance, students experienced either direct instruction (DI) or productive failure (PF), wherein they were first asked to generate a quantitative index for variance without any guidance before receiving DI on the concept. Whereas DI students relied only on the canonical…